The Cantor–Schröder–Bernstein Theorem for ∞-groupoids
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Colleges, School and Institutes
We show that the Cantor–Schröder–Bernstein Theorem for homotopy types, or ∞-groupoids, holds in the following form: For any two types, if each one is embedded into the other, then they are equivalent. The argument is developed in the language of homotopy type theory, or Voevodsky’s univalent foundations (HoTT/UF), and requires classical logic. It follows that the theorem holds in any boolean ∞-topos.
|Journal||Journal of Homotopy and Related Structures|
|Early online date||28 Jun 2021|
|Publication status||E-pub ahead of print - 28 Jun 2021|